I did intend to write a long post backing my ideas. However I lost my internet connection for most of this week, and am now threatened with a power failure.

I will only say that too much emphasis is placed on probability. Read Bernoulli's Theorem or D'Moivre's neither deal in facts. Only probabilities. Only with very large numbers can those probabilities be even close to facts.

I feel that in roulette or any gamble probability must bow to Statistics.

I did intend to write a long post backing my ideas. However I lost my internet connection for most of this week, and am now threatened with a power failure.

I will only say that too much emphasis is placed on probability. Read Bernoulli's Theorem or D'Moivre's neither deal in facts. Only probabilities. Only with very large numbers can those probabilities be even close to facts.

I feel that in roulette or any gamble probability must bow to Statistics.

Harry

I don't know why everyone is so focused on the triggers because that is only for short term protection and the relative reduction in expected max loss.

The objective reduction in the max loss is caused by the successive range betting; these act as sieves that improve the win rate because of the increased rarity of successive failures.

To me, there is a fundamental difference between trials and favorable cases....or probability versus "degrees of certainty" if you will. Probability represents the success ratio in only ONE trial. The degree of certainty measures the success ratio in a number of trials. Probability is static, whereas favorable cases are more fluid.

The problem is that according to experiment or experience there are limits, since none has ever observed 50 consecutive Blacks or 15 repeats of the same number on an unbiased wheel.

I believe that this video is one of the best arguments supporting the existence of limits in roulette.

Indeed it proves the point some of us have been trying to make for so long. If the experiment disagrees (which is non other than empirical observation), the assumption must be rejected. Though probability in not an assumption per se, it does assume that somewhere in the distant future or after several million spins, the unthinkable or extreme may happen. And if it happens so what? Are one or two rare exceptions going to compromise the vast majority of wins that came about simply by following the route of the empirical observation? (experiment).

The problem is that according to experiment or experience there are limits, since none has ever observed 50 consecutive Blacks or 15 repeats of the same number on an unbiased wheel.

I believe that this video is one of the best arguments supporting the existence of limits in roulette.

LOL. This is truly turning the tables on the theorists. Its true that they cannot demonstrate nor prove their theory, they can only claim that their theory is defined correctly which is recursive and contradictory.

1) wait for trigger2) bet range3) repeat 1 & 2 if no hit in range until hit is established in the range

Basically this is the way to program the simulation Reyth. But one problem is the trigger. In one roulette I may bet red after 10 Black (because that's what I happened to see when I walked up to that roulette.). In another roulette I may bet after seeing 6 black. In another after 12 odd. And this refers to EC triggers. It's not uncommon to play several different systems in the same session. Each having its own unique trigger. A trigger might form that requires to bet on one dozen or 2 dozens or 3 quads or 2-3 DS's. And out of the blue you play a different system. This means that the trigger is not constant. It varies all the time, because we observe many roulettes. And we can't place an order for a specific trigger like we place orders for pizza. What you see is what you have to deal with at that moment. And it can be different all the time. Only if you sit in one roulette you can wait for a specific trigger. Another problem is the issue of the bet amount. One day if I had a bad day at work I may decide to start out with very small chip. Another day I may decide to use the maximum starting chip that I can afford. Again you can't simulate something that depends on how you feel at the moment, because the conclusions drawn are not representative of the player's actual playing style. Also after a few successful bets I may decide to pull back and bet much lower. Believe it or not after a few successful consecutive attempts, you will find that most of the time things will get harder. In order to satisfy the player's own win/loss ratio. The opposite is also true. Harry can say a lot about this. The point is that VARIABLE SITUATIONS cannot be simulated. And it's best left to manual testing, to get more accurate results.

I will only say that too much emphasis is placed on probability. Read Bernoulli's Theorem or D'Moivre's neither deal in facts. Only probabilities. Only with very large numbers can those probabilities be even close to facts.

I feel that in roulette or any gamble probability must bow to Statistics.

Harry, it's not true that only with very large numbers can probabilities be close to the facts. It only takes a few thousand spins for the even chances to approximate very closely the theoretical probabilities.

And raw statistics, as everyone knows, can be manipulated or interpreted to mean anything. In fact they mean nothing unless interpreted. They don't stand on their own as objective facts. Reyth has interpreted his statistics to mean that virtual bets make a difference. I interpret them to mean the exact opposite.

1/2, 1/4, 1/8, 1/16, 1/32, etc are the probabilities of successive streaks. These are statistics, are they not? The value of each element is half the value of the previous element. How does this support the idea that it's better to start with the 4th element than the first, when the ratio between successive elements is constant?

What's being ignored is that it's the ratio of successive streaks that matters, not whether successive streaks diminish (which is true). A streak of 2 is to a streak of 1 what a streak of 5 is to a streak of 4, so wherever you start the chance of the next loss or win, or series of losses or wins, is the same. There's a factor of a half involved from streak to streak. Why is that so hard to understand?

As to limits, if there was a limit then the closer we get to whatever that limit is (be it 25 or whatever, for an EC), then the "distance" between successive streaks would diminish, so the ratio wouldn't be constant. The factor of a half, which was previously constant, would become a third, or a quarter, or a fifth. Where is the evidence for this? Do we see that it's far less likely that a streak of 10 will become a streak of 11 than it is for a streak of 2 to become a streak of 3, and increasingly less likely as the streaks get even longer?

No. And this has nothing to do with the tiny probability that anyone will actually see a streak of 40 reds in their lifetime, that's another red herring.

palestis, my question about the "spur of the moment" decisions was really a minor point. The point I would like to prove by the simulations is whether or not virtual bets have any impact on the number of losses and/or the variance.

You've offered an argument for the advantage of virtual bets:

Quote

Where betting black from the beginning (ignoring what came in the previous spins), means one thing and one thing only.That all the streaks of red that you frequently see on score boards, would've been lost money. Frequent opposite streaks would mean frequent losses.

Yes but this completely ignores the fact that you are missing out on the short streaks (prior to your triggers of 4 or more streaks). Or, if you are aware of this, you say the virtual bets give you a greater degree of security than just betting straight away from spin 1. But as I've previously explained (and you didn't disagree), it isn't the length of the streaks which matters but the relation between any given streak and the chance of it continuing or breaking, and this is the same whatever the streak length happens to be.

Yes I am well aware that I am missing out on winning opportunities. Which can be used against streaks that are not so friendly. I have had the same discussion with Mike about that some time ago. Many things are wrong with this line of thought.First of all you have to bet every spin. In doing so, you will lose due to the HE in the long run. That's the sad certainty. Any wins here and there will only be temporary.For that reason alone I wouldn't have to mention any other arguments against this style of play. But there is more.It's fine if you run into very short streaks. You can handle that. But if you run into a losing streak of 5, you will need to win 31 times just to recover one bad streak. If its 6 numbers streak you will need to win 63 times. 7 numbers streak you will need 127 wins to make up for it. Who in his right mind has the patience to wait for 31, 63 127 or more successful attempts, knowing that he will only break even? I wouldn't. Considering that streaks of 5 and 6 are frequent, most likely you will run into this situation in one session. And if you suffer another 5-6 number streak loss, forget about recovery anytime soon. Most players would give up playing that way. Can't you see the risk?Continuous betting loses to HE.Winning a friendly streak gets you single chip prizes. Losing an opposite streak you double quadruple octuple etc. your losses. Not a fair comparison. Now it's the turn of the virtual losses. First of all you have to set the minimum length of a streak that would count as virtual losses. You may set it at 5, but it could very well be that in another roulette you may run into an 8 number long streak. Or 10 or 12. Knowing that anything above 6 is getting to be rare, I can set my progression to just 3 spins. Where in the other case, there is no progression limit, or the limit is your entire B/R that is at risk.To lose that way here is what has to happen. A 6 number streak has to turn to a 10 number streak very often. Which it doesn't.A 7 number streak will have to become 11.An 8 numbers streak has to become 12. A 10 has to become 14. Very rare situations and when they happen all players gasp in awe.

Unless I am visually impaired, I simply never see those scenarios. Or if I see them they are very few and far between. Don't you see the advantage? In the previous scenario you bet every spin, and you double for an unknown numbers of spins. Which can be devastating if its long. In the second scenario, you scale your progression down to 3 steps, and you count on the fact that a streak of 10 + will not appear. And it usually doesn'tAnd if it does rarely, one thing is certain. It will not happen again in a consecutive fashion.

You just beat me to posting Palestis.A case here of “ And never the twain shall meet !

I think we have been over this ground before.

I think Bayes is right to say that Paley will lose out when the earlier spins would have given him a win. I think Palestis is also right to say “Yes, but I am willing to forgo them to lessen the bankroll needed when I do bet . And both my simulations and my actual betting confirm that “

You're saying that because no-one has ever seen 50 blacks in a row then random must have limits. What, in your view, are the limits? Suppose someone had the patience to wait for a streak and then bet against it with a 10 step martingale. What would the streak length have to be to guarantee a profit?

"Extreme event" records are being broken all the time, and as I've pointed out more than once, it isn't possible to do an "experiment" to test directly whether random has limits or not. After all, suppose I managed to find a streak of 50 reds, then you could just say "ah, but that doesn't prove there are no limits - find me a streak of 100 reds!".

Of course, as palestis says, the fact that long streaks and extreme events exist doesn't really have direct practical consequences, but it does have a bearing on virtual losses, which is why I included "Limits of Randomness" in the thread title.

If there were limits, then virtual losses would work, wouldn't they? This is one of the consequences of the proposition that "random has limits". So going back to the video and Feynman's 3 steps, we have:

1. Make a guess (random has limits).2. See what the guess would imply (virtual losses would make a difference).3. Compare consequences with nature/experiment/observation/experience.

Now, if the outcome of the experiment disagrees with the implications or consequences of the guess, then the guess was wrong. Which in this case means that if we show that virtual losses don't make a difference to your bottom line then random doesn't have limits.

We can't directly find any limits, because we don't have the luxury of having infinite time and resources, but we can still use the 3 step method to discover whether there are any practical limits, which is what anyone should be concerned about anyway.

“Yes, but I am willing to forgo them to lessen the bankroll needed when I do bet . And both my simulations and my actual betting confirm that “

Different strokes for different folks.

scep, you're assuming that there is a benefit to virtual losses and that this is that it lessens the bankroll needed. Why should it lessen the bankroll?

palestis is saying that it is safer to wait for a streak of 7 because "you hardly ever see streaks of 10". But having found a streak of 7, it is then no less likely that it will turn into a streak of 10 than a single will turn into a streak of 4. This is because, as I keeping saying (and people keep ignoring), the relationship between streaks of successive lengths is the same. And note that these very statistics are what Reyth keeps reminding us "naysayers" of!

So starting from bet 1, it is not more likely that you will encounter a streak of 3 against you than if you wait for a streak of 7. The chance of a streak of 3 against you has a fixed probability of 1/8, and that's it. The fallacy lies in thinking that because you often see streaks of 3 but hardly ever streaks of 10, then it must be better to start from a streak of 7. If you actually count up your wins and losses you'll see that there is no advantage.

@Kav,You're saying that because no-one has ever seen 50 blacks in a row then random must have limits. What, in your view, are the limits? Suppose someone had the patience to wait for a streak and then bet against it with a 10 step martingale. What would the streak length have to be to guarantee a profit?

Since we are walking on thin ice here, I believe that the best choice of words is important.I'm not saying that "random has limits" I'm saying "reality has limits". This is a more pragmatic approach than a scientific statement. Here is my view- I have carefully selected each word:

I believe that in the constrains of reality and given that I don't want to pass a math exam but I risk my own money, for all practical purposes there ARE limits to roulette extreme events.

I'm claiming nothing more (yet).

I'm not claiming that I know the exact limits, though 15 repeats of the same number or 50 consecutive Blacks seem out of limits and I would actually bet against them.

I'm not claiming I can use roulette limits to make money.It is one thing to have the insight/knowledge and a totally different thing to capitalize on it. Table limits, bankroll requirements, extremely long waiting time, low profit/spin ratio and various other factors can make it hard to create a useful winning system out of great ideas, facts, insights, observations and knowledge.

It's like the Martingale or the law of the third. For example bankroll and table limits make the Martingale non-viable while it is a great idea. IF we accept that in 200 spins one can encounter no more than 135 losses, this is great to know, but very hard to devise a method to make a profit.

This is why I believe that the discussion about how one can capitalize on the "roulette limits" is muddying the waters about the practical existence of them with all kinds of debates. Let us first decide if there are realistic limits in roulette and then we can discuss the consequences and the possible ways to exploit this fact.

"Extreme event" records are being broken all the time, and as I've pointed out more than once, it isn't possible to do an "experiment" to test directly whether random has limits or not.

It's neither that simple nor that easy to break a record of 100 years in even chances. You would need another 100 years just for 1 more consecutive spin. Read that post by Real . You may think that it supports your view of limitlessness but it also supports my view that realistic limits are what they are and you would need exponentially more trials to increase the limits by just one spin. Eventually you would reach the age of the universe and you would still have not exceeded all limits.

If there were limits, then virtual losses would work, wouldn't they? This is one of the consequences of the proposition that "random has limits". So going back to the video and Feynman's 3 steps, we have:

1. Make a guess (random has limits).2. See what the guess would imply (virtual losses would make a difference).3. Compare consequences with nature/experiment/observation/experience.

Now, if the outcome of the experiment disagrees with the implications or consequences of the guess, then the guess was wrong. Which in this case means that if we show that virtual losses don't make a difference to your bottom line then random doesn't have limits.

I don't agree. I understand your way of thinking and it seems to have some merit. But I don't agree that dismissing the value of virtual losses in everyday results will automatically dismiss the existence of roulette limits. It is perfectly possible that you can only gain an advantage if you push the outcomes into their extreme limits.

At the 10th or 15th consecutive spin there could always be a 50% chance of losing. But if you go for an extreme event your intention is that the losing streak will eventually lose. GF is about balance. One believes that the outcomes would start to balance out. Extreme limits are about... well limits, that there is an end. "It is due" is not the same with "it can't go further". You may miss the difference but it is there.

I firmly believe that the value of virtual losses (or past spins) is a related but different discussion that muddles the waters. You simply can not put someone who waits for 20 Blacks to bet on Red for another 20 spins on the same basket with someone who waits for 6 Blacks to bet on Red for the next 4 spins.

We can't directly find any limits, because we don't have the luxury of having infinite time and resources, but we can still use the 3 step method to discover whether there are any practical limits, which is what anyone should be concerned about anyway.

I don't care about theoretical limits of randomness. I give you that, let's say you are correct. It is irrelevant to my way of thinking. I care for realistic roulette limits and actual betting decisions.

Which one would you choose to bet your money on, as the most probable continuation of a 25 all Black sequence? What would be your answer? Why?

[...] Since we know the wheel is definitely not biased, I would choose the second sequence. But (and this is crucial), not because red is "due", but because a mix of red and black is more likely than all one colour, regardless of what has come before.

And here we come the meat. My friend Bayes, believe me, since you choose the 2nd sequence, there is no explanation for your decision other than you don't want to bet in favor of a rare near impossible event of sky-high-deviation. So in praxis you accept that there are limits. As most would do if one was to bet his own money. There is no possible explanation for choosing one over the other between two sequences of equal probability. Theoretically there is no reason at all (beyond "limits of reality") to choose the second sequence.

Trying to explain your choice you write that: "because a mix of red and black is more likely than all one colour". We are not talking about any mix though, we are talking about a very specific (in order) and extremely rare 50 spin sequence.And then you continue:"This doesn't contradict the fact that all sequences of the same length have the same probability, because in the case of a sequence the order of outcomes is taken into account. There are permutations and combinations; order matters for the former but not for the latter."

None is talking about combinations. We talk about a very specific sequence (specific order) that has the same probability with the all black sequence. Yet you bet your money on the non-all-black sequence. As I did. Because we both don't want to bet our money on a sky-high-deviation sequence that is beyond the so far known limits of roulette reality (not randomness).

To put it another way, both sequences are equally "rare", the only difference is that the all black sequence represents an out-of-this-world deviation from the mean - it is beyond any realistic limits.It is wise to not bet in favor of such deviation. This is why we both chose the other sequence.

PS: I will try to compose a post with the more interesting parts of this thread. I thoroughly enjoy this discussion.